If #tg^2alpha=3# then #sin^2(2alpha)# equal ...?

Question

If #tg^2alpha=3# then #sin^2(2alpha)# equal ...?

A) #3/4#
B) #1/2#
C) #1/4#
D) #1/8#

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Answer 1 · 2017-04-10T14:42:34

Given

#tan^2alpha=3#

#=>tanalpha=pmsqrt3#

Now

#sin2alpha=(2tanalpha)/(1+tan^2alpha)#

#=>sin2alpha=(pm2sqrt3)/(1+(pmsqrt3)^2)#

#=>sin2alpha=(pm2sqrt3)/4=pmsqrt3/2#

So

#sin^2 2alpha=(pmsqrt3/2)^2=3/4#